Math Problem Statement

Graph the linear equation 5x + 5y = 15.

Solution

The equation to graph is:

5x+5y=155x + 5y = 15

Steps to Graph the Equation:

  1. Simplify the equation: Divide the entire equation by 5 to simplify: x+y=3x + y = 3 Now, we have the equation in a simpler form.

  2. Rewrite in slope-intercept form: y=x+3y = -x + 3 This equation is in the form y=mx+by = mx + b, where:

    • m=1m = -1 is the slope (indicating a downward slope),
    • b=3b = 3 is the y-intercept (the point where the line crosses the y-axis).
  3. Plot the y-intercept:

    • Start by plotting the point (0, 3) on the y-axis.
  4. Use the slope:

    • The slope is -1, which means for every 1 unit you move to the right along the x-axis, move 1 unit down.
    • From the point (0, 3), move right 1 unit and down 1 unit to get the point (1, 2). Plot this point.
  5. Draw the line:

    • Draw a straight line through the points (0, 3) and (1, 2), extending in both directions.

Would you like me to generate a graph for this equation?

Follow-up Questions:

  1. What is the importance of slope-intercept form in graphing linear equations?
  2. How do you find the slope from a linear equation in standard form?
  3. What does the y-intercept tell you about the graph of a linear equation?
  4. Can you convert any linear equation into slope-intercept form?
  5. How can you check if a point lies on the graph of a linear equation?

Tip:

When graphing a linear equation, always start by identifying the y-intercept and the slope, as they provide a clear starting point and direction for the line.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing
Slope-Intercept Form

Formulas

Standard form of a linear equation: Ax + By = C
Slope-Intercept form: y = mx + b

Theorems

Linear graphing using slope and intercept

Suitable Grade Level

Grades 8-10